Accuracy vs Precision Precision – the exactness of a measurement. To how many decimal places is it measured out? Accuracy – how closely the measurement matches a known, accepted value. You can have one without the other: Ex: A rod is known to be 15.75 cm long. One student measures 17.248 cm, which is very precise, but not accurate. Another measures 16 cm, which is accurate, but not very precise. Better to have accuracy than precision Best if you can get both.

Precision in Measurements The precision of a measurement – how many decimal places it has been read out to – comes from the level of divisions on the tool you’re using to make the measurement. The rule is that you read a tool to the level at which is has 10 divisions, then you still need to make a guess between those divisions, and all those numbers are considered sig figs. 1. 20 cm – 1 sig fig 2. 22 cm – 2 sig figs 3. 22.2 cm – 3 sig figs With no divisions between 0 and 100, you can only guess that the line length is around 20 cm. 2 is our guess, 0 a place holder With 10 divisions between 1 and 100, we now can see it’s 20 something, so we make our guess as 22 or 23. With 10 more divisions, we can increase our precision to 22.2.

Determining Sig Figs Significant Figures are reliable digits because they’ve been measured accurately, through the process covered on the previous slide. don’t confuse the term “significant” with the idea of important, especially when it comes to 0’s. If the 0’s have to be there as place holders to give the number the correct value, that doesn’t make them a “sig fig” – often they’re not! For example: 23.01  4 23.015  5 23.010  5: the last zero shows the tool we were using could be measured out to that level of precision. 0.062  2, just the 6 and 2 0.0620  3, the 6, 2 and the trailing 0 1001  4 100  really only 1 as written, so…

That’s when scientific notation helps: 100 can be written as 1 x 102 to show just 1 sig fig 1.0 x 102 to show 2 sig figs, or 1.00 x 102 to show 3 sig fig. And 0.062 can be written as 6.2 x 10-2, which is easier to read. Rule: Write an answer in sci. not. if it’s: ≥ 10,000 OR < 0.01 (so 1/1000 column) Sig Figs in computations: +/- : Answer can’t have any more precision than the least precise number the answer came from. x/ : Answer can’t have any more sig figs than number with the least sig figs that the answer came from.

Units of Measurement The United States, at least in our daily lives, still uses a system that has its origin with the British Empire, hence its names: British Engineering System (BES) or British Imperial System (BIS) or English Engineering Units with base quantities of foot for length pound for weight (instead of one for mass) second for time, just to name a few

Most of the world uses a metric system known as SI (for International System, or reversed in French…) In physics, our standard within the metric system is known as the mks system since the units of its base quantities are meter (m) for length kilogram (kg) for mass second (s) for time. Also kelvin (K) for temperature mole (mol) for amount of something Coulomb (C) for electric charge candela (cd) for luminous intensity

Base quantities - those defined in terms of an absolute standard, such as the length of a second of time being defined as the time it takes the radiation emitted by a cesium atom to oscillate through 9,192,631,770 periods…whatever that means… Derived quantities – units of measurement that are combos of the 7 base quantities ex: m/s for speed liter for volume = length units3 Joule for energy = kg m2/s2 amps for electric current = Coulomb/s Note: base quantities are NOT meter, gram, liter; and derived quantities are NOT cm, kg, ml !

ESTIMATION Most important use of estimation in this class will be to use common sense and check your final answers before you box them in!! ex: 67.3 cm for distance to the moon 1874 s for air time on record frisbee throw 18 m/s for speed of cheetah chasing prey If you get an answer like one of these, write me a note telling me specifically why your answer doesn’t make sense, and I’ll give you some (sometimes it amounts to all!) points back in your solution.

Estimated metric to BES conversions 1 m ≈ 1 yd or 3 ft or 40” 1 km ≈ 2/3 mile 1 cm ≈ ½ inches or better 2.5 cm ≈ 1” 1 kg ≈ 2 lbs ≈ a textbook 1 g ≈ a paperclip x m/s ≈ 2x mph ≈ 4x km/h so x m/s x 2 ≈ ____ mph and x km/h ÷ 2 ≈ ____ mph Try some: 18.2 m/s ≈ 113.7 km/hr ≈ 346 m/s ≈ 43.7 km/h ≈

Expectations of Sig Figs In the lab: be very aware of and careful with sig figs in lab; follow all rules exactly. On homework & tests: keep at least 4 sig figs on values as you make your way through a problem, but then your final, boxed-in answer should just have 3 sig figs, unless it works out to be less precise than that. If the answer on the calculator is 4.5 or 20, that’s fine. But an answer of 8.399 is not… round it to ____ And what about 10378.4? ______